Influence of Vibrational Relaxation on the Pulsation Activity in Flows of an Excited Diatomic Gas

The influence of vibrational relaxation on the nonlinear evolution of a large vortex structure in a shear flow of a highly nonequilibrium diatomic gas is studied. Calculations are performed using the equations of twotemperature gas dynamics for a viscous heatconducting gas. Relaxation of the temperature of vibrational levels of gas molecules to equilibrium is described by the Landau–Teller equation. The contribution of the relaxation of rotational levels is taken into account by the bulk viscosity in the stress tensor. It is shown that in the presence of only the relaxation process with no viscous dissipation, the damping of the kinetic energy of perturbations and Reynolds stresses increases by up to 10 % compared to the case of thermal equilibrium. For high (actually attainable) degrees of excitation of the vibrational mode, moderate dynamic and bulk viscosities, and a typical relaxation time comparable to flow time, the relative effect of perturbation damping reaches 15%.     

Method of calculating subsonic gas flow with separation past wings

The steady nonlinear problem of subsonic compressible gas flow past a wing of arbitrary shape in plan is considered. A numerical method was devized for solving the problem; this is a further development of the method of discrete vortices. The surface of the body and the vortex wake behind it are simulated by systems of discrete vortex sections, but, in contrast to the case of an incompressible medium, it is necessary in this case for the sources to be distributed outside the wing. The circulations of the attached vortices, the strengths of the sources, and the shape of the wake are determined by iterations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 140–147, July–August, 1984.     

A spatial laminar boundary layer on a streamline in conical external flow of a uniform gas in the absence of sources and sinks

Theoretical study of a three-dimensional laminar boundary layer is a complex problem, but it can be substantially simplified in certain particular cases and even reduced to the solution of ordinary differential equations.One such particular case is the flow of a compressible gas on a streamline in conical external flow. The case is of considerable practical importance because the local heat fluxes may take extremal values on such lines.Such flow, except for the conical case, has been examined [1–4], and an approximate method has been given [1] on the basis of integral relationships and a special form for the approximating functions. A numerical solution has been given [2, 3] for such flow around an infinite cylinder. It was assumed in [1–3] that the Prandtl number and the specific heats were constant, and that the dynamic viscosity was proportional to temperature. Heat transfer has been examined [4] near a cylinder exposed to a flow of dissociated air.Here we give results from numerical solution of a system of ordinary differential equations for the flow of a compressible gas in a laminar boundary layer on streamlines in conical external flow, with or without influx or withdrawal of a homogeneous gas. It is assumed that the gas is perfect and that the dynamic viscosity has a power-law temperature dependence.     

A model for the bulk viscosity of a non-Newtonian fluid

A model for the bulk viscosity of a non-Newtonian fluid is presented. An elementary two-phase cell containing an incompressible non-Newtonian fluid and a gas bubble is compared with a one-phase cell consisting of a corresponding compressible non-Newtonian fluid. The rates of work of both cells are set equal to one another. The deformation histories of both cells are represented by the density history. From the extra stress an expression for the bulk viscosity of the compressible non-Newtonian fluid is derived. The material data are expressed in terms of the known properties of the two-phase flow.     

Energy Estimate of the Critical Reynolds Numbers in a Compressible Couette Flow. Effect of Bulk Viscosity

A variational problem of determining the critical Reynolds number of the laminar-turbulent transition is numerically solved within the framework of the nonlinear energy theory of stability of compressible flows. Stability of various modes in the Couette flow of a compressible gas is estimated by the method of collocations. It is demonstrated that the minimum critical Reynolds numbers in the range of the ratio of the bulk viscosity ηb to the shear viscosity η, which is realistic for diatomic gases, are reached for modes of streamwise disturbances. The critical Reynolds numbers increase as the bulk viscosity is increased in the interval η_b = 0-2η, with the maximum increase in the limit being approximately 30%.     

Interaction dynamics of two coaxial vortex rings in the presence of natural convection

The problem of the interaction of a pair of coaxial initially stationary thermals is investigated numerically on the basis of the Navier-Stokes equations for a compressible heat-conducting gas. It is established that upon transformation of the thermals into vortex rings, slip-through of the latter, limited in time because of the diffusion of vorticity and the action of molecular viscosity, is realized.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 169–171, July–August, 1991.     

Heat and mass transfer to a reacting particle in a gas flow for arbitrary temperature dependence of the transport coefficients

A study is made of simultaneous heat and mass transfer to a reacting particle of any shape in a translational (and shear) flow of a viscous heat conducting compressible gas for which the thermal conductivity and diffusion coefficient, and also the specific heat depend on the temperature. The first two terms of the asymptotic expansion with respect to the small Reynolds number are obtained for the mean Sherwood and Nusselt numbers. The case of a power-law temperature dependence of the gas viscosity is considered in detail.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–119, January–February, 1984.     

Homogenization of Wall-Slip Gas Flow Through Porous Media

The permeability of reservoir rocks is most commonly measured with an atmospheric gas. Permeability is greater for a gas than for a liquid. The Klinkenberg equation gives a semi-empirical relation between the liquid and gas permeabilities. In this paper, the wall-slip gas flow problem is homogenized. This problem is described by the steady state, low velocity Navier–Stokes equations for a compressible gas with a small Knudsen number. Darcy's law with a permeability tensor equal to that of liquid flow is shown to be valid to the lowest order. The lowest order wall-slip correction is a local tensorial form of the Klinkenberg equation. The Klinkenberg permeability is a positive tensor. It is in general not symmetric, but may under some conditions, which we specify, be symmetric. Our result reduces to the Klinkenberg equation for constant viscosity gas flow in isotropic media.     

Compressible and confined vortex flow

The internal compressible flow of a thin vortex chamber was investigated experimentally by measuring the radial distribution of temperature and pressure, from which the velocity field was calculated. The bulk of the internal vortex was found to be described by u_θr^0.69 = constant. The total resistance of the vortex chamber to the flow was also investigated in the context of fluidic vortex diode behavior under conditions of compressible and choked flow. It was found that the vortex chamber choked at an upstream-to-downstream pressure ratio of about 6 and in doing so passed a mass flow rate of 28% of the equivalent one-dimensional ideal nozzle. The resistance of vortex chambers is known to be strongly influenced by the presence of reversed flow in the exit due to vortex breakdown. Schlieren photography of the swirling exhaust flow was used to show that, while vortex breakdown does occur, it can only do so after the flow has become subsonic downstream of the exit and cannot therefore influence the vortex chamber resistance.     

Effect of supersonic stream parameters on the characteristic time of transient step flow

There have been many studies of viscous compressible gas flow in wakes and behind steps [1–6] in which attention has been focused on the steady-state flow regime. The problem of the supersonic flow of a viscous compressible heat-conducting gas past a plain backward-facing step is considered. The problem is solved numerically within the framework of the complete system of Navier-Stokes equations. The passage of the solution from the initial data to the steady-state regime and the effect of the gas dynamic parameters of the external flow on the characteristic flow stabilization time are investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–140, July–August, 1989.     

The bulk electroviscous effect

Electroviscous stresses arise as hydrodynamic flows disturb the ionic (Debye) clouds that screen charged surfaces in electrolyte solutions. The contribution thereof to the effective bulk viscosity (also known as the second or volume viscosity) of two-phase suspensions is quantified here. Specifically, the bulk viscosity of two model suspensions is calculated: (1) a dilute dispersion of rigid charged spherical particles immersed in a compressible electrolyte that undergoes uniform dilatation and (2) a dilute suspension of charged gas bubbles expanding uniformly in an incompressible electrolyte. In both cases, it is assumed that the fluid flow only slightly drives the Debye cloud out of equilibrium, which formally requires that the ratio of the ion diffusion to flow time scales—a Péclet number—is small. For a suspension of rigid particles, the electroviscous contribution to the effective bulk viscosity is proportional to the particle volume fraction and decreases monotonically as the ratio of the particle radius to the Debye length increases. Similar behavior is well known for the electroviscous contribution to the effective shear viscosity of a dilute hard-sphere suspension; a quantitative comparison between the bulk and shear viscosities is made. In contrast, the electroviscous contribution to the bulk viscosity of a dilute suspension of bubbles is independent of the bubble volume fraction and attains a finite value in the limit of vanishing Debye length.     

Downstream boundary effects on the spectral characteristics of a swirling flowfield

The spectral characteristics and the structural response of a swirling flowfield are investigated subject to a non-axisymmetric disturbance and a contraction imposed downstream. Two natural frequencies are noted in different regions of the undisturbed swirling flowfield, one is due to a precessing vortex core and the other to the most amplified downstream azimuthal instability. The downstream contraction usually causes compression of the central recirculation zone into two side-lobes, increases the dominant frequencies and forms a straight central vortex core with a high axial velocity. The dominant downstream instability frequency depends linearly on the inlet Reynolds number and on the mode of the breakdown. For the downstream non-axisymmetric disturbance, such as the passing of the turbine blades, the fundamental frequency is not altered by the disturbance and the oscillation strength of the downstream instability is greatly reduced as the excitation frequency remains unmatched with the dominant downstream natural frequency. Downstream azimuthal instability promotes the breakdown recirculation.A version of this paper was presented at the 26th AIAA Aerospace Sciences Meeting, Reno, Nevada, 11–14, Jan. 1988     

Fast numerical evaluation of flow fields with vortex cells

A vortex cell (in this paper) is an aerodynamically shaped cavity in the surface of a body, for example a wing, designed specially to trap the separated vortex within it, thus preventing large-scale unsteady vortex shedding from the wing. Vortex stabilisation can be achieved either by the special geometry, as has already been done experimentally, or by a system of active control. In realistic conditions the boundary and mixing layers in the vortex cell are always turbulent. In the present study a model for calculating the flow in a vortex cell was obtained by replacing the laminar viscosity with the turbulent viscosity in the known high-Reynolds-number asymptotic theory of steady laminar flows in vortex cells. The model was implemented numerically and was shown to be faster than solving the Reynolds-averaged Navier–Stokes equations. An experimental facility with a vortex cell was built and experiments performed. Comparisons of the experimental results with the predictions of the model are reasonably satisfactory. The results also indicate that at least for flows in near-circular vortex cells it is sufficient to have accurate turbulence models only in thin viscous layers, while outside the viscosity should only be small enough to make the flow effectively inviscid.     

A THEORETICAL ANALYSIS OF THE FLOW DISTURBANCE INDUCED BY A SPHERE OSCILLATING IN INCOMPRESSIBLE FLUID

为了改进基于不可压缩流场的声类比法的气动声数值预测方法,首先要明确扰动在可压缩和不可压缩流体媒介中的传播特性. 推导了震荡小球在不可压缩流体中产生的小扰动的理论解,分析其速度场与压力场的特点,并与可压缩情况的解进行比较. 结果显示,速度场中包含传播速度为无穷大和有限值的分量;而压力场只有传播速度为无穷大的分量. 当流体黏性趋于零或小球震荡频率趋于无穷大时,其流场与经典声学中震荡小球声辐射问题的近场声一致,这表明震荡小球产生的近场扰动为不可压缩流场,即伪声.     

Effect of bulk viscosity on Kelvin-Helmholtz instability

An energy functional leading to a resolvable variational problem for determining the critical Reynolds number of laminar-turbulent transition Re _cr is constructed within the framework of the nonlinear energy stability theory of compressible flows. Asymptotic estimates containing the characteristic dependence in the main order are obtained for the stability of various modes of Couette compressible gas flow. The asymptotics considered are long-wave approximations. This suggests that the obtained dependence describes the effect of bulk viscosity on the large-scale vortex structures characteristic of Kelvin-Helmholtz instability. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 73–84, May–June, 2008.     

Analysis of flow in an annular duct with large injection at the walls

Viscous heat-conducting compressible fluid flow in an annular duct formed by two coaxial cylinders with large injection at the walls is investigated. An asymptotic solution exhibiting the influence of the axial symmetry of the duct is obtained in the vicinity of the y axis and is compared with the results of exact numerical calculations. Asymptotic solutions of the Navier-Stokes equations have been obtained earlier for flows in a plane channel with various rates of wall injection in the case of an incompressible gas [1, 2] and a compressible gas [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 135–139, May–June, 1976.     

Subsonic flow of a compressible gas around a semiinfinite flat plate in a pipe

The subsonic flow of an ideal compressible gas around the rear end of a semiinfinite flat plate in a pipe is considered. The flow pattern is similar to that assumed by Efros [1, 2] with a return stream for the cavitational flows. Fal'kovich's method [3] is used to solve the problem and this makes it possible to obtain the solution to the problems of the gas streams at several typical velocities. The method is a generalization of that of Chaplygin [4] for flow problems at one typical velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 101–108, July–August, 1970.     

Linear stability of the Couette flow of a vibrationally excited gas. 2. viscous problem

Based on the linear theory, stability of viscous disturbances in a supersonic plane Couette flow of a vibrationally excited gas described by a system of linearized equations of two-temperature gas dynamics including shear and bulk viscosity is studied. It is demonstrated that two sets are identified in the spectrum of the problem of stability of plane waves, similar to the case of a perfect gas. One set consists of viscous acoustic modes, which asymptotically converge to even and odd inviscid acoustic modes at high Reynolds numbers. The eigenvalues from the other set have no asymptotic relationship with the inviscid problem and are characterized by large damping decrements. Two most unstable viscous acoustic modes (I and II) are identified; the limits of these modes were considered previously in the inviscid approximation. It is shown that there are domains in the space of parameters for both modes, where the presence of viscosity induces appreciable destabilization of the flow. Moreover, the growth rates of disturbances are appreciably greater than the corresponding values for the inviscid flow, while thermal excitation in the entire considered range of parameters increases the stability of the viscous flow. For a vibrationally excited gas, the critical Reynolds number as a function of the thermal nonequilibrium degree is found to be greater by 12% than for a perfect gas.     

Acceleration of a gas compressed under conditions of acuteangled geometry

In obtaining high velocities (10–100 km/sec) by methods employing the mechanical motion of compressible media it is customary to use the flow scheme obtained with shaped charges [1–4]. This paper presents the results of a study of an apparatus that can be used to obtain gas jets in the same velocity range but at higher densities by means of a different type of flow.     

A visual study of vortex-induced subcritical instability on a flat plate laminar boundary layer

This paper reports results of our experimental investigation on flow instability on a flat plate laminar boundary layer caused by a captive vortex migrating far outside the boundary layer. Results show that the sign of the circulation associated with the vortex is the main determinant for the severity of the boundary layer instability. A captive vortex with an opposite sign to that of the unperturbed shear layer vorticity causes a breakdown ahead of it, while the one with the same sign as the unperturbed shear layer vorticity gives rise to weaker excitation trailing it. Additional parameters that influence the flow instability are the strength and distance of the vortical disturbance from the boundary layer, as well as the translational speed of the vortex. These experimental results compliment the corresponding theoretical analysis of Sengupta et al. (J Fluid Mech 493:277–286, 2003).